Answer:
x² + x - 30Step-by-step explanation:
Let the initial side be x
New skatepark has dimensions:
x - 5 and x + 6Its area is:
(x - 5)(x + 6) = x² + 6x - 5x - 30 = x² + x - 30Need Help with this please!!
Answer:
A is 85 degrees
Jamal wants to install a rectangular 2025 cm² window in his garden shed. That area of window comes in several length/width combinations, and he wants to minimize the perimeter to prevent drafts. What is the least perimeter possible for the window?
Answer:
The ideal size will be a 45cmx45cm square, giving you a perimeter of 180cm.
Step-by-step explanation:
The shortcut answer here is that the square will always be the most efficient rectangle for border to area, so the sides should be the square root of 2025 cm, or 45 cm each, giving you a total of 180 minimum perimeter.
The full solution is to express the perimeter as a function of the length and width, define either length or width as a function of the other, take the entire expression's derivative and solve for zero. Let's do it:
So first the area:
2025 = wl
l = 2025 / w
Now the sides:
[tex]p = 2w + 2l\\p = 2w + 2(2025 / w)\\p = 2w + 4050 / w[/tex]
Then we can take its derivative with respect to w
[tex]p = 2w + 4050\frac{1}{w}\\\frac{dp}{dw} = 2 + 4050\frac{-1}{w^2}\\[/tex]
Now we can set the derivative to zero, and solve for w:
[tex]\frac{dp}{dw} = 2 + 4050\frac{-1}{w^2}\\0 = 2 + \frac{-4050}{w^2}\\-2 = \frac{-4050}{w^2}\\2w^2 = 4050\\w^2 = 2025\\w = \sqrt{2025}\\w = 45[/tex]
So the width being 45, we can get the length by dividing the area by that amount, which of course is also 45.
Twice the difference of 1 and a number.
consider the two functions which statement is true?
Answer:
A
Step-by-step explanation:
In a certain year, the average e-mail user sent or received 111 e-mails each day. The number of e-mails received was 3 more than twice the number
sent. How many were sent and how many were received each day?
Answer:
Number of sent mail = 36
Number of received mail = 75
Step-by-step explanation:
Let,
x be the number of mails sent
y be the number of mails received
According to given statement;
x + y = 111 Eqn 1
y = 2x + 3 Eqn 2
Putting value of y from Eqn 2 in Eqn 1
x + 2x + 3 = 111
3x = 111 - 3
3x = 108
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{108}{3}\\x = 36[/tex]
Putting x = 36 in Eqn 2
y = 2(36) + 3
y = 72 + 3 = 75
Hence,
Number of sent mail = 36
Number of received mail = 75
What is the measure of angle P?
Answer:
60
Step-by-step explanation:
step 1: 180°-130°= 50
step 2: 180-110= 70
step 3: 70+50= 120
step 4: 180°-120°= 60
Help pls question is the picture above :))))
Juan received a bank account statement reporting the recent changes
to his account. The statement showed an overall increase in the
account balance of $1,909.15. During the time shown on the
statement, Juan was paid twice and withdrew a total of $1,437.99 to
cover all his bills and expenses. How much (x) is each of Juan's
paychecks?
Answer:
2628.15
Step-by-step explanation:
1909.15+ 1437.99/2=2628.15
Mae has a number cube with 6 sides that are numbered 1 through 6. What is the probability that Mae will roll an odd number?
A
1 out of 3
B
1 out of 6
с
3 out of 6
D
5 out of 6
Answer:
C) [tex]P(E) = \frac{3}{6}[/tex]
The probability that Mae will roll an odd number
[tex]P(E) = \frac{3}{6}[/tex]
Step-by-step explanation:
Step(i):-
Given that Mae has a number cube with 6 sides that are numbered 1 through 6.
n(S) = { 1,2,3,4,5,6,} = 6
Let 'E ' be the event of odd numbers
Mae will roll an odd number
n(E) = {1, 3, 5} = 3
Step(ii):-
The probability that Mae will roll an odd number
[tex]P(E) = \frac{n(E)}{n(S)} = \frac{3}{6}[/tex]
[tex]P(E) = \frac{3}{6}[/tex]
(ONLY MY FRIENDS RESPOND) What is the Area of a square if it has L= 32cm and W= 20cm?
(Heres a re-made thing for my friends, sorry for the rushed handwriting, I had to do it before my mom saw, hope u guys can read it)
Answer:
640
Step-by-step explanation: and wow
Solve the linear equation x + 4 + 3x = 72. State the property that justifies your first step and why you chose it
Please Help!!!!!!!!!
Answer:
x=17
Step-by-step explanation:
x+4+3x=72
4x+4-4=72-4
4x/4=68/4
x=17
Associative property of addition
Answer: x = 17
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Plsssss helpppppppppp meeeeeeeeee
Answer:
x = 14, y = 37
Step-by-step explanation:
The angle vertical to (9x + 12 )° and 3x are same- side interior angles and are supplementary, sum to 180°, then
9x + 12 + 3x = 180
12x + 12 = 180 ( subtract 12 from both sides )
12x = 168 ( divide both sides by 12 )
x = 14, so
3x = 3 × 14 = 42
3x and 4y - 10 are adjacent angles and supplementary, then
3x + 4y - 10 = 180
42 + 4y - 10 = 180
4y + 32 = 180 ( subtract 32 from both sides )
4y = 148 ( divide both sides by 4 )
y = 37
please solve for b
a=b/c
Answer:
b = ac
Step-by-step explanation:
Solve for b by simplifying both sides of the equation, then isolating the variable.
Answer:
b= ac
Solve for b by simplifying both sides of the equation, then isolating the variable.
A pair of jeans that originally cost $40 was marked up 50%. During a sale the jeans were discounted 50%. What
is the sale price?
Can you explain how to show my work step by step
Answer:
20$
Step-by-step explanation:
50% of 40= 20
I need to write an equation for the triangle and solve for x
The. Ordered pair?
Is this a function yes or no?
The Texas Renaissance Festival charges an entrance fee of $10 and $0.50 per ticket for the rides. The State Fair of Texas charges an entrance fee of $16 and requires $0.25 per ticket for the rides. How many tickets must be bought in order for the total cost at The Texas Renaissance Festival to be the same as The State Fair of Texas?
a
8
b
24
c
16
d
12
Number seven plz helppp
Answer:
1,296
Step-by-step explanation:
I multiplied 6 four times.
In the last 40 days, Mr. Neptune's newspaper has been delivered late 6 times. What is the experimental probability that it will be delivered late tomorrow?
Answer:
15%
Step-by-step explanation:
The reason for this is simply because if you take 40 and 6, turn it into a fraction, then turn it into a percentage, it turns out to be 15%
John spent $75 on a shopping trip for new clothes last week. He had expected to spend $100 on clothes,
Approximate Value Exact Value Error Absolute Error Ratio Percent Error
$100
$75
$25
How much was the absolute error in his estimate?
$
Intro
Answer:
Absolute error = $25
Step-by-step explanation:
Given that:
Amount spent by John on shopping trip = $75
Estimated amount to spent on shopping trip = $100
Absolute error = Approximate value - Exact value
Here,
Approximate value = $100
Exact value = $75
Absolute error = 100 - 75
Absolute error = $25
Percentage = [tex]\frac{Absolute\ error}{Exact\ value}*100[/tex]
Percentage = [tex]\frac{25}{75}*100[/tex]
Percentage = 33.33%
Hence,
Absolute error = $25
If GEOM is a square, find m2GQE.
Answer:
90 is correct answer of it question
The volume of a cylinder is 1767 cm and its height is 11 cm.
What is the length of the cylinder's radius?
Enter your answer in the box.
Answer:
1778 cm
Step-by-step explanation:
The ordered pairs (8,12). (16, 24), (x, 21), (26, y) represent a proportional relationship
Find the value of x and the value of y.
Select the two correct answers.
A y=56
B. x= 14
C. x=7
D. y=39
Ex= 9
F. y = 42
Answer: B. x= 14
D. y=39
Step-by-step explanation:
First and foremost, we need to calculate the constant of proportionality. This will be:
(8,12).
y = kx.
12 = 8k
k = 12/8
k = 1.5
(16, 24),
y = kx
24 = 16k
k = 24/16
k = 1.5
(x, 21),
y = kx
x = y/k
x = 21/1.5
x = 14
(26, y)
y = kx
y = 26 × 1.5
y = 39
what is the slope of the form of (1,2) m= -2
Answer:
m = -2
Step-by-step explanation:
slope is m in y = mx + b
You already said what m is
What is the simplified form of the expression(x + 6)(7x − 1)?
8x^2 + 5
7x^2 + 41x − 6
7x^2 + 43x − 6
7x^2 − 6
Answer:c
Step-by-step explanation:
Answer:
B: 7x2 + 41x − 6
Step-by-step explanation:
Use the FOIL method to multiply the two expressions.
(First Outer Inner Last)
Then, combine like terms.
(x + 6)(7x − 1) = (x)(7x) + (x)(-1) + (6)(7x) + (6)(-1)
= 7x2 − x + 42x − 6
= 7x2 + 41x − 6
The diagram shows two congruent equilateral triangles whose overlap is a hexagon.
The areas of the smaller triangles, which are also equilateral, are 1, 1, 9, 9, 16 and 16, as shown.
16
16
X1
9
What is the area of the inner hexagon?
Answer:
38
Step-by-step explanation:
What hazard is present in this image?
Select the best option.
A mat that has upturned edges
Hair clippings on the floor
Tool cord left out
Spills on floor
Answer:
spills on the floor
Step-by-step explanation:
there is liquid of some sort someone could slip and hurt themselves. hope this helps
reduce to the simplest form[tex]\frac{286}{858}[/tex]
Answer:
143 over 428
Step-by-step explanation:
can someone please help me?
Which of the following expressions will result in a product less than zero?
А
6.4 x (-3.5)
B
-7.1 x (2.5)
С
-2.3 (-1.9)
D
9.2 x (4.0)
Answer:
All of the except for D and C
Step-by-step explanation:
A negative times a positive is always negative
Answer:
A,B
Step-by-step explanation:
